tl;dr - No, it's a new creation for the movies, based on an idea in the comics they can't use.
The Quantum Realm is the Marvel Cinematic Universe version of The Microverse, as it's referred to in the comics. They don't have the film rights to the name, as it was used most often (and fleshed out the most) in the Micronauts comics, and they don't have those rights anymore.
Various versions of the Microverse have appeared in other comics, like the Fantastic Four, into which Doctor Doom disappears in an early adventure. Jarella's World in The Hulk was a micro-world as well.
In the comics, the Microverse is technically a parallel dimension that one passes into once someone shrinks past a certain threshold.
Since they couldn't use the Microverse, they adapted / created the Quantum Realm, which shares some of the same DNA with the comics version, but a lot of new ideas. All of the ideas of time anomalies and the like were whipped up for the films.
Tardigrades are a real thing, tho.
Doctor Strange witnesses the Quantum Realm for a moment in his film as he is made to pass through various dimensions and mystical zones.
There's a number of fan theories that the Quantum Realm, the energy found within it, and those very hand-wavy at the moment time anomalies will play a major role in Avengers 4, and the plot to defeat Thanos.